58
Chapter 2
EXERCISE SET 2.5 1. (a) no, x = 2 (e) yes
(b) no, x = 2 (f ) yes
(c) no, x = 2
(d) yes
2. (a) no, x = 2 (e) no, x = 2
(b) no, x = 2 (f ) yes
(c) no, x = 2
(d) yes
3. (a) no, x = 1, 3 (e) no, x = 3
(b) yes (f ) yes
(c) no, x = 1
(d) yes
4. (a) no, x = 3 (e) no, x = 3
(b) yes (f ) yes
(c) yes
(d) yes
5. (a) At x = 3 the one-sided limits fail to exist. (b) At x = −2 the two-sided limit exists but is not equal to F (−2). (c) At x = 3 the limit fails to exist. 6. (a) At x = 2 the two-sided limit fails to exist. (b) At x = 3 the two-sided limit exists but is not equal to F (3). (c) At x = 0 the two-sided limit fails to exist. 7. (a) 3
8. −2/5
(b) 3 y
9. (a)
y
(b)
1 x
x 1
3
(c)
y
(d)
1
3
y
x 1
x 2
3
-1
10. f (x) = 1/x, g(x) =
11. (a)
0
if x = 0
1 sin x
if x = 0 (b) One second could cost you one dollar.
C
$4 t 1
2